What is the integral of cos(x/8) ?

The integral of cos(x/8) is 8sin(x/8)+C

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integral of cos(x/8)

\int cos (\frac{x}{8}) d x

8 sin (\frac{x}{8}) + C

Solution steps

\int cos (\frac{x}{8}) d x

Apply u-substitution

: \int cos (u) \cdot 8 d u

= \int cos (u) \cdot 8 d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 8 \cdot \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= 8 sin (u)

Substitute back

u = \frac{x}{8}

= 8 sin (\frac{x}{8})

Add a constant to the solution

= 8 sin (\frac{x}{8}) + C

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